Finite Group Databasebeta

← Group #11778189

Character table — Group #11778189

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222444444444444448888888888888888888888888121224242424242424242424242424242424242424484872727272
order12222233666666666634466666666612124412121212121212121212121212121212121212121212124422224666666881212242424246124488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111-1-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1
χ611111111111111111111111111111111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-111111111-1-1-1-111
χ711111111111111111111111111111111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-111
χ811111111111111111111111111111111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-111-1-1
χ92222222222222222222-2-2222222222-2-200-2-2-20000-2-2-2-200000000000022-20000-2-2000000220000000000
χ102222222222222222222-2-2222222222-2-200-2-2-20000-2-2-2-2000000000000-2-22000022000000-2-20000000000
χ112222222-12-1-1-12-1-1-12-1-1222-1-1-1-12-1-1-122222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222200-1-1-1-1-1-100-1-10000000000
χ122222222-12-1-1-12-1-1-12-1-1222-1-1-1-12-1-1-122222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-20011111100110000000000
χ132222222-12-1-1-12-1-1-12-1-1222-1-1-1-12-1-1-122-2-22-1-11111-1-1-1-1-2-2-2-211111111222-2-200-1-1111100-1-10000000000
χ142222222-12-1-1-12-1-1-12-1-1222-1-1-1-12-1-1-122-2-22-1-11111-1-1-1-1-2-2-2-211111111-2-2-2220011-1-1-1-100110000000000
χ152222222-12-1-1-12-1-1-12-1-1-2-22-1-1-1-12-1-1-1-2-200-211−i3−i3i3i311110000−i3−i3−i3−i3i3i3i3i322-2000011−i3−i3i3i300-1-10000000000
χ162222222-12-1-1-12-1-1-12-1-1-2-22-1-1-1-12-1-1-1-2-200-211−i3−i3i3i311110000−i3−i3−i3−i3i3i3i3i3-2-220000-1-1i3i3−i3−i300110000000000
χ172222222-12-1-1-12-1-1-12-1-1-2-22-1-1-1-12-1-1-1-2-200-211i3i3−i3−i311110000i3i3i3i3−i3−i3−i3−i322-2000011i3i3−i3−i300-1-10000000000
χ182222222-12-1-1-12-1-1-12-1-1-2-22-1-1-1-12-1-1-1-2-200-211i3i3−i3−i311110000i3i3i3i3−i3−i3−i3−i3-2-220000-1-1−i3−i3i3i300110000000000
χ19222222-12-1222-1222-12-122-1-1-1-1-1-1-1-1-1-1-122-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000220000002200-1-1-1-1-1-10000
χ20222222-12-1222-1222-12-122-1-1-1-1-1-1-1-1-1-1-122-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000-2-2000000-2-2001111110000
χ21222222-12-1222-1222-12-122-1-1-1-1-1-1-1-1-1-1-1-2-2-122-2-2-2-2-1-1-1-11111111111110000022000000-2-2001111-1-10000
χ22222222-12-1222-1222-12-122-1-1-1-1-1-1-1-1-1-1-1-2-2-122-2-2-2-2-1-1-1-111111111111100000-2-20000002200-1-1-1-1110000
χ232222-2-22222-2-222-2-22222-2-222-2-2-22-2-22200-22-2000022-2-2000000000000000000000000000000000002-200
χ242222-2-22222-2-222-2-22222-2-222-2-2-22-2-22200-22-2000022-2-200000000000000000000000000000000000-2200
χ252222-2-22222-2-222-2-2222-22-222-2-2-22-2-2-2-2002-220000-2-222000000000000000002-2000000000000002-20000
χ262222-2-22222-2-222-2-2222-22-222-2-2-22-2-2-2-2002-220000-2-22200000000000000000-2200000000000000-220000
χ272222-2-2-12-12-2-2-12-2-2-12-1-221-1-1111-1111100-1-22000011-1-133−3−333−3−333−3−3000002-2000000000033−3−3-110000
χ282222-2-2-12-12-2-2-12-2-2-12-1-221-1-1111-1111100-1-22000011-1-133−3−333−3−333−3−300000-220000000000−3−3331-10000
χ292222-2-2-12-12-2-2-12-2-2-12-1-221-1-1111-1111100-1-22000011-1-1−3−333−3−333−3−333000002-20000000000−3−333-110000
χ302222-2-2-12-12-2-2-12-2-2-12-1-221-1-1111-1111100-1-22000011-1-1−3−333−3−333−3−33300000-22000000000033−3−31-10000
χ3122-2-22-222-2222-2-2-2-22-220022-222-2-2-2-20000000000000000000000000002i−2i00000000000−i2i22i−2i−i2i2−i2i200002−2
χ3222-2-22-222-2222-2-2-2-22-220022-222-2-2-2-20000000000000000000000000002i−2i00000000000i2−i22i−2ii2−i2i2−i20000−22
χ3322-2-22-222-2222-2-2-2-22-220022-222-2-2-2-2000000000000000000000000000−2i2i00000000000−i2i2−2i2i−i2i2−i2i20000−22
χ3422-2-22-222-2222-2-2-2-22-220022-222-2-2-2-2000000000000000000000000000−2i2i00000000000i2−i2−2i2ii2−i2i2−i200002−2
χ35444444-24-2444-2444-24-2-4-4-2-2-2-2-2-2-2-2-222002-4-400002222000000000000000000000000000000000000000
χ36444444-2-2-2-2-2-2-2-2-2-2-2-2144-21111-2111-2-244-2-2-2-2-2-2-21111-2-2-2-211111111000000000000000000000000000
χ37444444-2-2-2-2-2-2-2-2-2-2-2-2144-21111-2111-2-2-4-4-2-2-2222211112222-1-1-1-1-1-1-1-1000000000000000000000000000
χ38444444-2-2-2-2-2-2-2-2-2-2-2-21-4-4-21111-21112200222−2i3−2i32i32i3-1-1-1-10000i3i3i3i3−i3−i3−i3−i3000000000000000000000000000
χ39444444-2-2-2-2-2-2-2-2-2-2-2-21-4-4-21111-211122002222i32i3−2i3−2i3-1-1-1-10000−i3−i3−i3−i3i3i3i3i3000000000000000000000000000
χ404444-4-44-24-2224-2224-2-24-4-4-2-222-4-2224400-4-220000-2-222000000000000000000000000000000000000000
χ414444-4-44-24-2224-2224-2-2-44-4-2-222-4-222-4-40042-2000022-2-2000000000000000000000000000000000000000
χ424444-4-4-24-24-4-4-24-4-4-24-24-42-2-2222-222-2-20024-40000-2-222000000000000000000000000000000000000000
χ434444-4-4-2-2-2-222-2-222-2-214-4211-1-121-1-1-2-2002-22000011-1-100003i3i−3i−3i−3i−3i3i3i000000000000000000000000000
χ444444-4-4-2-2-2-222-2-222-2-214-4211-1-121-1-1-2-2002-22000011-1-10000−3i−3i3i3i3i3i−3i−3i000000000000000000000000000
χ454444-4-4-2-2-2-222-2-222-2-21-44211-1-121-1-12200-22-20000-1-1112323−23−23−3−333−3−333000000000000000000000000000
χ464444-4-4-2-2-2-222-2-222-2-21-44211-1-121-1-12200-22-20000-1-111−23−23232333−3−333−3−3000000000000000000000000000
χ4744-4-44-44-2-4-2-2-2-422242-2004-22-2-2-42220000000000000000000000000004i−4i0000000000000−2i2i0000000000
χ4844-4-44-44-2-4-2-2-2-422242-2004-22-2-2-4222000000000000000000000000000−4i4i00000000000002i−2i0000000000
χ4944-4-44-4-2424442-4-4-4-2-4-200-2-22-2-222220000000000000000000000000000000000000000−2i22i200i2−i2i2−i2000000
χ5044-4-44-4-2424442-4-4-4-2-4-200-2-22-2-2222200000000000000000000000000000000000000002i2−2i200−i2i2−i2i2000000
χ5144-4-4-4444-44-4-4-4-4444-4400-44-4-4-44-444000000000000000000000000000000000000000000000000000000
χ5244-4-4-444-2-4-222-42-2-242-200-4-222242-2-20000000000000000000000000000000000−2i32i3000000000000000000
χ5344-4-4-444-2-4-222-42-2-242-200-4-222242-2-200000000000000000000000000000000002i3−2i3000000000000000000
χ5444-4-4-44-2424-4-42-444-2-4-2002-2222-22-2-200000000000000000000000000000000000000000000i6−i6−i6i6000000
χ5544-4-4-44-2424-4-42-444-2-4-2002-2222-22-2-200000000000000000000000000000000000000000000−i6i6i6−i6000000
χ564-44-40044-4-4004400-4-44000-4-40004000000000000000000000000000000002-200002-22-200000000000000
χ574-44-40044-4-4004400-4-44000-4-4000400000000000000000000000000000000-220000-22-2200000000000000
χ584-44-4004-2-42−2i32i34-2−2i32i3-42-200022−2i32i30-2−2i32i30000000000000000000000000000002-20000−1−i31+i3−1+i31−i300000000000000
χ594-44-4004-2-42−2i32i34-2−2i32i3-42-200022−2i32i30-2−2i32i3000000000000000000000000000000-2200001+i3−1−i31−i3−1+i300000000000000
χ604-44-4004-2-422i3−2i34-22i3−2i3-42-2000222i3−2i30-22i3−2i30000000000000000000000000000002-20000−1+i31−i3−1−i31+i300000000000000
χ614-44-4004-2-422i3−2i34-22i3−2i3-42-2000222i3−2i30-22i3−2i3000000000000000000000000000000-2200001−i3−1+i31+i3−1−i300000000000000
χ624-4-4400444-400-4-400-444000-44000-400002-20002-22-200002-22-22-22-22-22-2000000000000000000000000000
χ634-4-4400444-400-4-400-444000-44000-40000-22000-22-220000-22-22-22-22-22-22000000000000000000000000000
χ644-4-44004-242−2i32i3-422i3−2i3-4-2-20002-2−2i32i3022i3−2i3002-2000−1−i31+i3−1+i31−i300002-22-2−1−i31+i3−1−i31+i3−1+i31−i3−1+i31−i3000000000000000000000000000
χ654-4-44004-242−2i32i3-422i3−2i3-4-2-20002-2−2i32i3022i3−2i300-220001+i3−1−i31−i3−1+i30000-22-221+i3−1−i31+i3−1−i31−i3−1+i31−i3−1+i3000000000000000000000000000
χ664-4-44004-2422i3−2i3-42−2i32i3-4-2-20002-22i3−2i302−2i32i3002-2000−1+i31−i3−1−i31+i300002-22-2−1+i31−i3−1+i31−i3−1−i31+i3−1−i31+i3000000000000000000000000000
χ674-4-44004-2422i3−2i3-42−2i32i3-4-2-20002-22i3−2i302−2i32i300-220001−i3−1+i31+i3−1−i30000-22-221−i3−1+i31−i3−1+i31+i3−1−i31+i3−1−i3000000000000000000000000000
χ684-4-4400-24-2-4002-40024-20002-200020023−232-20002-22-223−2300−1+31−3−1−31+3−1+31−3−1−31+3−1+31−3−1−31+3000000000000000000000000000
χ694-4-4400-24-2-4002-40024-20002-200020023−23-22000-22-2223−23001−3−1+31+3−1−31−3−1+31+3−1−31−3−1+31+3−1−3000000000000000000000000000
χ704-4-4400-24-2-4002-40024-20002-2000200−23232-20002-22-2−232300−1−31+3−1+31−3−1−31+3−1+31−3−1−31+3−1+31−3000000000000000000000000000
χ714-4-4400-24-2-4002-40024-20002-2000200−2323-22000-22-22−2323001+3−1−31−3−1+31+3−1−31−3−1+31+3−1−31−3−1+3000000000000000000000000000
χ724-4-4400-2-2-22−2i32i3222i3−2i32-21000-11i3−i30-1−i3i323−232-2000−1−i31+i3−1+i31−i3−333i−3i−1+31−3−1−31+3ζ4−ζ14−2ζ22−ζ4+ζ14+2ζ22ζ4+ζ14+2ζ22−ζ4−ζ14−2ζ222ζ14+ζ20+ζ22−2ζ14−ζ20−ζ22−2ζ14+ζ20−ζ222ζ14−ζ20+ζ22000000000000000000000000000
χ734-4-4400-2-2-22−2i32i3222i3−2i32-21000-11i3−i30-1−i3i323−23-220001+i3−1−i31−i3−1+i3−333i−3i1−3−1+31+3−1−3−ζ4+ζ14+2ζ22ζ4−ζ14−2ζ22−ζ4−ζ14−2ζ22ζ4+ζ14+2ζ22−2ζ14−ζ20−ζ222ζ14+ζ20+ζ222ζ14−ζ20+ζ22−2ζ14+ζ20−ζ22000000000000000000000000000
χ744-4-4400-2-2-22−2i32i3222i3−2i32-21000-11i3−i30-1−i3i3−23232-2000−1−i31+i3−1+i31−i33−3−3i3i−1−31+3−1+31−3ζ4+ζ14+2ζ22−ζ4−ζ14−2ζ22ζ4−ζ14−2ζ22−ζ4+ζ14+2ζ22−2ζ14+ζ20−ζ222ζ14−ζ20+ζ222ζ14+ζ20+ζ22−2ζ14−ζ20−ζ22000000000000000000000000000
χ754-4-4400-2-2-22−2i32i3222i3−2i32-21000-11i3−i30-1−i3i3−2323-220001+i3−1−i31−i3−1+i33−3−3i3i1+3−1−31−3−1+3−ζ4−ζ14−2ζ22ζ4+ζ14+2ζ22−ζ4+ζ14+2ζ22ζ4−ζ14−2ζ222ζ14−ζ20+ζ22−2ζ14+ζ20−ζ22−2ζ14−ζ20−ζ222ζ14+ζ20+ζ22000000000000000000000000000
χ764-4-4400-2-2-222i3−2i322−2i32i32-21000-11−i3i30-1i3−i323−232-2000−1+i31−i3−1−i31+i3−33−3i3i−1+31−3−1−31+32ζ14+ζ20+ζ22−2ζ14−ζ20−ζ22−2ζ14+ζ20−ζ222ζ14−ζ20+ζ22ζ4−ζ14−2ζ22−ζ4+ζ14+2ζ22ζ4+ζ14+2ζ22−ζ4−ζ14−2ζ22000000000000000000000000000
χ774-4-4400-2-2-222i3−2i322−2i32i32-21000-11−i3i30-1i3−i323−23-220001−i3−1+i31+i3−1−i3−33−3i3i1−3−1+31+3−1−3−2ζ14−ζ20−ζ222ζ14+ζ20+ζ222ζ14−ζ20+ζ22−2ζ14+ζ20−ζ22−ζ4+ζ14+2ζ22ζ4−ζ14−2ζ22−ζ4−ζ14−2ζ22ζ4+ζ14+2ζ22000000000000000000000000000
χ784-4-4400-2-2-222i3−2i322−2i32i32-21000-11−i3i30-1i3−i3−23232-2000−1+i31−i3−1−i31+i33−33i−3i−1−31+3−1+31−3−2ζ14+ζ20−ζ222ζ14−ζ20+ζ222ζ14+ζ20+ζ22−2ζ14−ζ20−ζ22ζ4+ζ14+2ζ22−ζ4−ζ14−2ζ22ζ4−ζ14−2ζ22−ζ4+ζ14+2ζ22000000000000000000000000000
χ794-4-4400-2-2-222i3−2i322−2i32i32-21000-11−i3i30-1i3−i3−2323-220001−i3−1+i31+i3−1−i33−33i−3i1+3−1−31−3−1+32ζ14−ζ20+ζ22−2ζ14+ζ20−ζ22−2ζ14−ζ20−ζ222ζ14+ζ20+ζ22−ζ4−ζ14−2ζ22ζ4+ζ14+2ζ22−ζ4+ζ14+2ζ22ζ4−ζ14−2ζ22000000000000000000000000000
χ8088-8-88-8-4-44-4-4-44444-44200-42-2224-2-2-2000000000000000000000000000000000000000000000000000000
χ8188-8-8-88-4-44-44444-4-4-4420042-2-2-2-4-222000000000000000000000000000000000000000000000000000000
χ828-88-800-484-800-48004-8-400044000-400000000000000000000000000000000000000000000000000000000
χ838-88-800-4-444−4i34i3-4-4−4i34i3442000-2-22i3−2i3022i3−2i3000000000000000000000000000000000000000000000000000000
χ848-88-800-4-4444i3−4i3-4-44i3−4i3442000-2-2−2i32i302−2i32i3000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.